integral from 0 to 2 of x^2sqrt(x^3+5)

Lösung

\int_{0}^{2} x^{2} x^{3} + 5 d x

\frac{26 13 - 10 5}{9}

Dezimale

7.93151 \dots

Schritte zur Lösung

\int_{0}^{2} x^{2} x^{3} + 5 d x

Wende U-Substitution an

= \int_{5}^{13} \frac{u}{3} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int_{5}^{13} u d u

Wende die Potenzregel an

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{13}

Berechne die Grenzen:

\frac{26 13 - 10 5}{3}

= \frac{1}{3} \cdot \frac{26 13 - 10 5}{3}

Vereinfache

= \frac{26 13 - 10 5}{9}

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